http://www.ukm.my/kamal3/psm/pfpstochastics.pdf

The stochastic finite element method: Past, present and future

Optimization algorithms for structural reliability

A new method for efficient discretization of random fields (i.e., their representation in terms of random variables) is introduced. The efficiency of the discretization is measured by the number of random variables required to represent the field with a specified level of accuracy. The method is based on principles of optimal linear estimation theory. It represents the field as a linear function of nodal random variables and a set of shape functions, which are determined by minimizing an error variance. Further efficiency is achieved by spectral decomposition of the nodal covariance matrix. The new method is found to be more efficient than other existing discretization methods, and more practical than a series expansion method employing the Karhunen‐Loeve theorem. The method is particularly useful for stochastic finite element studies involving random media, where there is a need to reduce the number of random variables so that the amount of required computations can be reduced.

Optimal discretization of random fields

Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations

A new method for the solution of problems involving material variability is proposed. The material property is modeled as a stochastic process. The method makes use of the Karhunen‐Loeve expansion to represent the random material property. The expansion is a representation of the process in terms of a finite set of uncorrelated random variables. The resulting formulation is compatible with the finite element method. A Neumann expansion scheme is subsequently employed to obtain a convergent expansion of the response process. The response is thus obtained as a homogeneous multivariate polynomial in the uncorrelated random variables. From this representation various statistical quantities may be derived. The usefulness of the proposed method, in terms of accuracy and efficiency, is exemplified by considering a cantilever beam with random rigidity. The derived results pertaining to the second‐order statistics of the response are found in good agreement with those obtained by a Monte Carlo simulation solution ...

Jyh-Bin Ke

Papers

The stochastic finite element method in structural reliability